{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 机器学习工程师纳米学位\n",
    "## 模型评价与验证\n",
    "## 项目 1: 预测波士顿房价\n",
    "\n",
    "\n",
    "欢迎来到机器学习的预测波士顿房价项目！在此文件中，有些示例代码已经提供给你，但你还需要实现更多的功能来让项目成功运行。除非有明确要求，你无须修改任何已给出的代码。以**编程练习**开始的标题表示接下来的内容中有需要你必须实现的功能。每一部分都会有详细的指导，需要实现的部分也会在注释中以**TODO**标出。请仔细阅读所有的提示！\n",
    "\n",
    "除了实现代码外，你还**必须**回答一些与项目和实现有关的问题。每一个需要你回答的问题都会以**'问题 X'**为标题。请仔细阅读每个问题，并且在问题后的**'回答'**文字框中写出完整的答案。你的项目将会根据你对问题的回答和撰写代码所实现的功能来进行评分。\n",
    "\n",
    ">**提示：**Code 和 Markdown 区域可通过 **Shift + Enter** 快捷键运行。此外，Markdown可以通过双击进入编辑模式。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第一步. 导入数据\n",
    "在这个项目中，你将利用马萨诸塞州波士顿郊区的房屋信息数据训练和测试一个模型，并对模型的性能和预测能力进行测试。通过该数据训练后的好的模型可以被用来对房屋做特定预测---尤其是对房屋的价值。对于房地产经纪等人的日常工作来说，这样的预测模型被证明非常有价值。\n",
    "\n",
    "此项目的数据集来自[UCI机器学习知识库(数据集已下线)](https://archive.ics.uci.edu/ml/datasets.html)。波士顿房屋这些数据于1978年开始统计，共506个数据点，涵盖了麻省波士顿不同郊区房屋14种特征的信息。本项目对原始数据集做了以下处理：\n",
    "- 有16个`'MEDV'` 值为50.0的数据点被移除。 这很可能是由于这些数据点包含**遗失**或**看不到的值**。\n",
    "- 有1个数据点的 `'RM'` 值为8.78. 这是一个异常值，已经被移除。\n",
    "- 对于本项目，房屋的`'RM'`， `'LSTAT'`，`'PTRATIO'`以及`'MEDV'`特征是必要的，其余不相关特征已经被移除。\n",
    "- `'MEDV'`特征的值已经过必要的数学转换，可以反映35年来市场的通货膨胀效应。\n",
    "\n",
    "运行下面区域的代码以载入波士顿房屋数据集，以及一些此项目所需的 Python 库。如果成功返回数据集的大小，表示数据集已载入成功。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston housing dataset has 489 data points with 4 variables each.\n"
     ]
    }
   ],
   "source": [
    "# Import libraries necessary for this project\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import ShuffleSplit\n",
    "\n",
    "# Import supplementary visualizations code visuals.py\n",
    "import visuals as vs\n",
    "\n",
    "# Pretty display for notebooks\n",
    "%matplotlib inline\n",
    "\n",
    "# Load the Boston housing dataset\n",
    "data = pd.read_csv('housing.csv')\n",
    "prices = data['MEDV']\n",
    "features = data.drop('MEDV', axis = 1)\n",
    "    \n",
    "# Success\n",
    "print(\"Boston housing dataset has {} data points with {} variables each.\".format(*data.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第二步. 分析数据\n",
    "在项目的第一个部分，你会对波士顿房地产数据进行初步的观察并给出你的分析。通过对数据的探索来熟悉数据可以让你更好地理解和解释你的结果。\n",
    "\n",
    "由于这个项目的最终目标是建立一个预测房屋价值的模型，我们需要将数据集分为**特征(features)**和**目标变量(target variable)**。\n",
    "- **特征** `'RM'`， `'LSTAT'`，和 `'PTRATIO'`，给我们提供了每个数据点的数量相关的信息。\n",
    "- **目标变量**：` 'MEDV'`，是我们希望预测的变量。\n",
    "\n",
    "他们分别被存在 `features` 和 `prices` 两个变量名中。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 1：基础统计运算\n",
    "你的第一个编程练习是计算有关波士顿房价的描述统计数据。我们已为你导入了 ` NumPy `，你需要使用这个库来执行必要的计算。这些统计数据对于分析模型的预测结果非常重要的。\n",
    "在下面的代码中，你要做的是：\n",
    "- 计算 `prices` 中的 `'MEDV'` 的最小值、最大值、均值、中值和标准差；\n",
    "- 将运算结果储存在相应的变量中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics for Boston housing dataset:\n",
      "\n",
      "Minimum price: $105000.00\n",
      "Maximum price: $1024800.00\n",
      "Mean price: $454342.94\n",
      "Median price $438900.00\n",
      "Standard deviation of prices: $165171.13\n"
     ]
    }
   ],
   "source": [
    "# TODO: Minimum price of the data\n",
    "minimum_price = np.array(prices).min()\n",
    "\n",
    "# TODO: Maximum price of the data\n",
    "maximum_price = np.array(prices).max()\n",
    "\n",
    "# TODO: Mean price of the data\n",
    "mean_price = np.array(prices).mean()\n",
    "\n",
    "# TODO: Median price of the data\n",
    "median_price = np.median(np.array(prices))\n",
    "\n",
    "# TODO: Standard deviation of prices of the data\n",
    "std_price = np.array(prices).std()\n",
    "\n",
    "# Show the calculated statistics\n",
    "print(\"Statistics for Boston housing dataset:\\n\")\n",
    "print(\"Minimum price: ${:.2f}\".format(minimum_price)) \n",
    "print(\"Maximum price: ${:.2f}\".format(maximum_price))\n",
    "print(\"Mean price: ${:.2f}\".format(mean_price))\n",
    "print(\"Median price ${:.2f}\".format(median_price))\n",
    "print(\"Standard deviation of prices: ${:.2f}\".format(std_price))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 特征观察\n",
    "\n",
    "如前文所述，本项目中我们关注的是其中三个值:`'RM'`、`'LSTAT'` 和`'PTRATIO'`，对每一个数据点:\n",
    "- `'RM'` 是该地区中每个房屋的平均房间数量；\n",
    "- `'LSTAT'` 是指该地区有多少百分比的业主属于是低收入阶层（有工作但收入微薄）；\n",
    "- `'PTRATIO'` 是该地区的中学和小学里，学生和老师的数目比（`学生/老师`）。\n",
    "\n",
    "_凭直觉，上述三个特征中对每一个来说，你认为增大该特征的数值，`'MEDV'`的值会是**增大**还是**减小**呢？每一个答案都需要你给出理由。_\n",
    "\n",
    "**提示：**你预期一个`'RM'` 值是6的房屋跟`'RM'` 值是7的房屋相比，价值更高还是更低呢？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 回答：\n",
    "\n",
    "其他因素相同的情况下，当然是房屋房间数越多，房价越贵\n",
    "\n",
    "如果地区低收入阶层的业主比较多，说明该地区欠发达，所以房价比较低\n",
    "\n",
    "如果该地区学生与老师数目比比较高，则一个学生对应的老师数比较低，说明该地区教育不发达，房价会比较低。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第三步. 建立模型\n",
    "在项目的第三步中，你需要了解必要的工具和技巧来让你的模型进行预测。用这些工具和技巧对每一个模型的表现做精确的衡量可以极大地增强你预测的信心。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习2：定义衡量标准\n",
    "如果不能对模型的训练和测试的表现进行量化地评估，我们就很难衡量模型的好坏。通常我们会定义一些衡量标准，这些标准可以通过对某些误差或者拟合程度的计算来得到。在这个项目中，你将通过运算[决定系数](https://en.wikipedia.org/wiki/Coefficient_of_determination) $R^2$ 来量化模型的表现。模型的决定系数是回归分析中十分常用的统计信息，经常被当作衡量模型预测能力好坏的标准。\n",
    "\n",
    "$R^2$ 的数值范围从0至1，表示**目标变量**的预测值和实际值之间的相关程度平方的百分比。一个模型的 $R^2$ 值为0还不如直接用**平均值**来预测效果好；而一个 $R^2$ 值为1的模型则可以对目标变量进行完美的预测。从0至1之间的数值，则表示该模型中目标变量中有百分之多少能够用**特征**来解释。模型也可能出现负值的 $R^2$，这种情况下模型所做预测有时会比直接计算目标变量的平均值差很多。\n",
    "\n",
    "在下方代码的 `performance_metric` 函数中，你要实现：\n",
    "- 使用 `sklearn.metrics` 中的 [`r2_score`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.r2_score.html) 来计算 `y_true` 和 `y_predict` 的 $R^2$ 值，作为对其表现的评判。\n",
    "- 将他们的表现评分储存到 `score` 变量中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO: Import 'r2_score'\n",
    "from sklearn.metrics import r2_score\n",
    "def performance_metric(y_true, y_predict):\n",
    "    \"\"\" Calculates and returns the performance score between \n",
    "        true and predicted values based on the metric chosen. \"\"\"\n",
    "    \n",
    "    # TODO: Calculate the performance score between 'y_true' and 'y_predict'\n",
    "    score=r2_score(y_true,y_predict)\n",
    "    \n",
    "    # Return the score\n",
    "    return score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 拟合程度\n",
    "\n",
    "假设一个数据集有五个数据且一个模型做出下列目标变量的预测：\n",
    "\n",
    "| 真实数值 | 预测数值 |\n",
    "| :-------------: | :--------: |\n",
    "| 3.0 | 2.5 |\n",
    "| -0.5 | 0.0 |\n",
    "| 2.0 | 2.1 |\n",
    "| 7.0 | 7.8 |\n",
    "| 4.2 | 5.3 |\n",
    "*你觉得这个模型已成功地描述了目标变量的变化吗？如果成功，请解释为什么，如果没有，也请给出原因。*  \n",
    "\n",
    "**提示1**：运行下方的代码，使用 `performance_metric` 函数来计算 `y_true` 和 `y_predict` 的决定系数。\n",
    "\n",
    "**提示2**：$R^2$ 分数是指可以从自变量中预测的因变量的方差比例。 换一种说法：\n",
    "\n",
    "* $R^2$ 为0意味着因变量不能从自变量预测。\n",
    "* $R^2$ 为1意味着可以从自变量预测因变量。\n",
    "* $R^2$ 在0到1之间表示因变量可预测的程度。\n",
    "* $R^2$ 为0.40意味着 Y 中40％的方差可以从 X 预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model has a coefficient of determination, R^2, of 0.923.\n"
     ]
    }
   ],
   "source": [
    "# Calculate the performance of this model\n",
    "score = performance_metric([3, -0.5, 2, 7, 4.2], [2.5, 0.0, 2.1, 7.8, 5.3])\n",
    "print(\"Model has a coefficient of determination, R^2, of {:.3f}.\".format(score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 回答:\n",
    "\n",
    "可以，决定系数比较大"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 3: 数据分割与重排\n",
    "接下来，你需要把波士顿房屋数据集分成训练和测试两个子集。通常在这个过程中，数据也会被重排列，以消除数据集中由于顺序而产生的偏差。\n",
    "在下面的代码中，你需要\n",
    "\n",
    "* 使用 `sklearn.model_selection` 中的 `train_test_split`， 将 `features` 和 `prices` 的数据都分成用于训练的数据子集和用于测试的数据子集。\n",
    "  - 分割比例为：80%的数据用于训练，20%用于测试；\n",
    "  - 选定一个数值以设定 `train_test_split` 中的 `random_state` ，这会确保结果的一致性；\n",
    "* 将分割后的训练集与测试集分配给 `X_train`, `X_test`, `y_train` 和 `y_test`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training and testing split was successful.\n"
     ]
    }
   ],
   "source": [
    "# TODO: Import 'train_test_split'\n",
    "from sklearn.model_selection import train_test_split\n",
    "# TODO: Shuffle and split the data into training and testing subsets\n",
    "X_train, X_test, y_train, y_test = train_test_split(features, prices, test_size = 0.2,random_state=20)\n",
    "\n",
    "# Success\n",
    "print(\"Training and testing split was successful.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 训练及测试\n",
    "*将数据集按一定比例分为训练用的数据集和测试用的数据集对学习算法有什么好处？*\n",
    "\n",
    "*如果用模型已经见过的数据，例如部分训练集数据进行测试，又有什么坏处？*\n",
    "\n",
    "**提示：** 如果没有数据来对模型进行测试，会出现什么问题？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 回答:\n",
    "分为数据集和测试集是为了让模型尽可能学习到更普遍的规律，防止模型仅仅学到了数据集的特点和规律，导致其泛化性能差\n",
    "\n",
    "使用部分测试集进行测试会产生模型适用性强的假象，当使用其他数据后表现能力会变差。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第四步. 分析模型的表现\n",
    "在项目的第四步，我们来看一下不同参数下，模型在训练集和验证集上的表现。这里，我们专注于一个特定的算法（带剪枝的决策树，但这并不是这个项目的重点），和这个算法的一个参数 `'max_depth'`。用全部训练集训练，选择不同`'max_depth'` 参数，观察这一参数的变化如何影响模型的表现。画出模型的表现来对于分析过程十分有益。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 学习曲线\n",
    "下方区域内的代码会输出四幅图像，它们是一个决策树模型在不同最大深度下的表现。每一条曲线都直观得显示了随着训练数据量的增加，模型学习曲线的在训练集评分和验证集评分的变化，评分使用决定系数 $R^2$。曲线的阴影区域代表的是该曲线的不确定性（用标准差衡量）。\n",
    "\n",
    "运行下方区域中的代码，并利用输出的图形回答下面的问题。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sWbN6u+tfffXV/Q444ID9Bw8ePPrtt99OAygqKvKdfPLJQ4YMGTJq0qRJ+44e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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22e71ef9fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Produce learning curves for varying training set sizes and maximum depths\n",
    "vs.ModelLearning(features, prices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 学习曲线\n",
    "* 选择上述图像中的其中一个，并给出其最大深度。\n",
    "* 随着训练数据量的增加，训练集曲线的评分有怎样的变化？验证集曲线呢？\n",
    "* 如果有更多的训练数据，是否能有效提升模型的表现呢？\n",
    "\n",
    "**提示：**学习曲线的评分是否最终会收敛到特定的值？一般来说，你拥有的数据越多，模型表现力越好。但是，如果你的训练和测试曲线以高于基准阈值的分数收敛，这是否有必要？基于训练和测试曲线已经收敛的前提下，思考添加更多训练点的优缺点。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 回答:\n",
    "\n",
    "最大深度为3时的模型较好\n",
    "\n",
    "训练数据增加，训练集曲线评分变低，验证集曲线评分变高，最后两者都趋于稳定的值\n",
    "\n",
    "对于深度3来说，由于训练和验证集曲线趋于收敛，更多的训练点数据作用不大，只会增加计算成本，使用更多训练集在学习曲线收敛前作用比较明显"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 复杂度曲线\n",
    "下列代码内的区域会输出一幅图像，它展示了一个已经经过训练和验证的决策树模型在不同最大深度条件下的表现。这个图形将包含两条曲线，一个是训练集的变化，一个是验证集的变化。跟**学习曲线**相似，阴影区域代表该曲线的不确定性，模型训练和测试部分的评分都用的 `performance_metric` 函数。\n",
    "\n",
    "**运行下方区域中的代码，并利用输出的图形并回答下面的问题5与问题6。**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Yz77z0ag9x1ApKoJwODcVF8OMGf1Fz2XDhtHflx1QUOEzxnxuB9sNcFYh66AoilJQhmpV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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22e76054240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vs.ModelComplexity(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 偏差（bias）与方差（variance）之间的权衡取舍\n",
    "* 当模型以最大深度 1训练时，模型的预测是出现很大的偏差还是出现了很大的方差？\n",
    "* 当模型以最大深度10训练时，情形又如何呢？\n",
    "* 图形中的哪些特征能够支持你的结论？\n",
    "\n",
    "\n",
    "**提示：** 高偏差表示欠拟合（模型过于简单），而高方差表示过拟合（模型过于复杂，以至于无法泛化）。考虑哪种模型（深度1或10）对应着上述的情况，并权衡偏差与方差。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 回答:\n",
    "\n",
    "最大深度为1，模型预测偏差比较大，R2评分较低\n",
    "\n",
    "最大深度为10时，方差较高，训练集和验证集曲线相差较大"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 6- 最优模型的猜测\n",
    "* 结合问题 5 中的图，你认为最大深度是多少的模型能够最好地对未见过的数据进行预测？\n",
    "* 你得出这个答案的依据是什么？\n",
    "\n",
    "\n",
    "**提示**：查看问题5上方的图表，并查看模型在不同 `depth`下的验证分数。随着深度的增加模型的表现力会变得更好吗？我们在什么情况下获得最佳验证分数而不会使我们的模型过度复杂？请记住，奥卡姆剃刀：“在竞争性假设中，应该选择假设最少的那一个。”"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 6 - 回答:\n",
    "\n",
    "深度为4，此时训练和验证曲线趋于收敛并且此时R2评分较大\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第五步. 评估模型的表现\n",
    "在项目的最后一节中，你将构建一个模型，并使用 `fit_model` 中的优化模型去预测客户特征集。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 7- 网格搜索（Grid Search）\n",
    "* 什么是网格搜索法？\n",
    "* 如何用它来优化模型？\n",
    "\n",
    "**提示**：在解释网格搜索算法时，首先要理解我们为什么使用网格搜索算法，以及我们使用它的最终目的是什么。为了使你的回答更具有说服力，你还可以给出一个模型中可以使用此方法进行优化参数的示例。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 7 - 回答:\n",
    "\n",
    "网格搜索算法是一种通过遍历给定的参数组合来优化模型表现的方法。\n",
    "在决策树算法中需要确定决策树的最大深度，例如对于深度1，使用K折交叉验证得到验证分数，同理对2，3，4···10深度得到分数，分数最大的就是最优分数。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 8 - 交叉验证\n",
    "- 什么是K折交叉验证法（k-fold cross-validation）？\n",
    "- [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) 是如何结合交叉验证来完成对最佳参数组合的选择的？\n",
    "- [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) 中的`'cv_results_'`属性能告诉我们什么？\n",
    "- 网格搜索为什么要使用K折交叉验证？K折交叉验证能够避免什么问题？\n",
    "\n",
    "**提示**：在解释k-fold交叉验证时，一定要理解'k'是什么，和数据集是如何分成不同的部分来进行训练和测试的，以及基于'k'值运行的次数。\n",
    "在考虑k-fold交叉验证如何帮助网格搜索时，你可以使用特定的数据子集来进行训练与测试有什么缺点，以及K折交叉验证是如何帮助缓解这个问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 8 - 回答：\n",
    "\n",
    "K次交叉验证，将训练集分割成K个子样本，一个单独的子样本被保留作为验证模型的数据，其他K-1个样本用来训练。交叉验证重复K次，每个子样本验证一次，平均K次的结果或者使用其它结合方式，最终得到一个单一估测。\n",
    "\n",
    "使用交叉验证得到不同参数组合下的分数，分数最高者组合为最优参数\n",
    "\n",
    "以字典的形式存放不同超参数的组合方式及其计算结果\n",
    "\n",
    "交叉验证可以评估模型的预测性，能在一定程度上减小过拟合。还可以从有限的数据中获取尽可能多的有效信息。\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 4：拟合模型\n",
    "在这个练习中，你将需要将所学到的内容整合，使用**决策树算法**训练一个模型。为了得出的是一个最优模型，你需要使用网格搜索法训练模型，以找到最佳的 `'max_depth'` 参数。你可以把`'max_depth'` 参数理解为决策树算法在做出预测前，允许其对数据提出问题的数量。决策树是**监督学习算法**中的一种。\n",
    "\n",
    "另外，你会发现在实现的过程中是使用`ShuffleSplit()`作为交叉验证的另一种形式（参见'cv_sets'变量）。虽然它不是你在问题8中描述的K-fold交叉验证方法，但它同样非常有用！下面的`ShuffleSplit()`实现将创建10个('n_splits')混洗集合，并且对于每个混洗集，数据的20％（'test_size'）将被用作验证集合。当您在实现代码的时候，请思考一下它与 `K-fold cross-validation` 的不同与相似之处。\n",
    "\n",
    "请注意，`ShuffleSplit` 在 `Scikit-Learn` 版本0.17和0.18中有不同的参数。对于下面代码单元格中的 `fit_model` 函数，您需要实现以下内容：\n",
    "\n",
    "1. **定义 `'regressor'` 变量**: 使用  `sklearn.tree` 中的 [`DecisionTreeRegressor`](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeRegressor.html) 创建一个决策树的回归函数;\n",
    "2. **定义 `'params'` 变量**: 为 `'max_depth'` 参数创造一个字典，它的值是从1至10的数组;\n",
    "3. **定义 `'scoring_fnc'` 变量**: 使用 `sklearn.metrics` 中的 [`make_scorer`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.make_scorer.html)  创建一个评分函数。将 `‘performance_metric’` 作为参数传至这个函数中；\n",
    "4. **定义 `'grid'` 变量**: 使用 `sklearn.model_selection` 中的 [`GridSearchCV`](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) 创建一个网格搜索对象；将变量`'regressor'`, `'params'`, `'scoring_fnc'`和 `'cv_sets'` 作为参数传至这个对象构造函数中；\n",
    "\n",
    "  \n",
    "如果你对 Python 函数的默认参数定义和传递不熟悉，可以参考这个MIT课程的[视频](http://cn-static.udacity.com/mlnd/videos/MIT600XXT114-V004200_DTH.mp4)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO: Import 'make_scorer', 'DecisionTreeRegressor', and 'GridSearchCV'\n",
    "from sklearn.metrics import make_scorer\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "def fit_model(X, y):\n",
    "    \"\"\" Performs grid search over the 'max_depth' parameter for a \n",
    "        decision tree regressor trained on the input data [X, y]. \"\"\"\n",
    "    \n",
    "    # Create cross-validation sets from the training data\n",
    "    # sklearn version 0.18: ShuffleSplit(n_splits=10, test_size=0.1, train_size=None, random_state=None)\n",
    "    # sklearn versiin 0.17: ShuffleSplit(n, n_iter=10, test_size=0.1, train_size=None, random_state=None)\n",
    "    cv_sets = ShuffleSplit(n_splits=10, test_size=0.20, random_state=42)\n",
    "    \n",
    "    # TODO: Create a decision tree regressor object\n",
    "    regressor = DecisionTreeRegressor(random_state=42)\n",
    "\n",
    "    # TODO: Create a dictionary for the parameter 'max_depth' with a range from 1 to 10\n",
    "    params = {'max_depth':[1,2,3,4,5,6,7,8,9,10]}\n",
    "\n",
    "    # TODO: Transform 'performance_metric' into a scoring function using 'make_scorer' \n",
    "    scoring_fnc = make_scorer(performance_metric)\n",
    "\n",
    "    # TODO: Create the grid search cv object --> GridSearchCV()\n",
    "    # Make sure to include the right parameters in the object:\n",
    "    # (estimator, param_grid, scoring, cv) which have values 'regressor', 'params', 'scoring_fnc', and 'cv_sets' respectively.\n",
    "    grid = GridSearchCV(regressor, params, scoring=scoring_fnc,cv=cv_sets)\n",
    "\n",
    "    # Fit the grid search object to the data to compute the optimal model\n",
    "    grid = grid.fit(X, y)\n",
    "\n",
    "    # Return the optimal model after fitting the data\n",
    "    return grid.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第六步. 做出预测\n",
    "当我们用数据训练出一个模型，它现在就可用于对新的数据进行预测。在决策树回归函数中，模型已经学会对新输入的数据*提问*，并返回对**目标变量**的预测值。你可以用这个预测来获取数据未知目标变量的信息，这些数据必须是不包含在训练数据之内的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 9 - 最优模型\n",
    "*最优模型的最大深度（maximum depth）是多少？此答案与你在**问题 6**所做的猜测是否相同？*\n",
    "\n",
    "运行下方区域内的代码，将决策树回归函数代入训练数据的集合，以得到最优化的模型。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter 'max_depth' is 4 for the optimal model.\n"
     ]
    }
   ],
   "source": [
    "# Fit the training data to the model using grid search\n",
    "reg = fit_model(X_train, y_train)\n",
    "\n",
    "# Produce the value for 'max_depth'\n",
    "print(\"Parameter 'max_depth' is {} for the optimal model.\".format(reg.get_params()['max_depth']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 9 - 回答：\n",
    "\n",
    "最大深度为4，与问题6猜测相同"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 10 - 预测销售价格\n",
    "想像你是一个在波士顿地区的房屋经纪人，并期待使用此模型以帮助你的客户评估他们想出售的房屋。你已经从你的三个客户收集到以下的资讯:\n",
    "\n",
    "| 特征 | 客戶 1 | 客戶 2 | 客戶 3 |\n",
    "| :---: | :---: | :---: | :---: |\n",
    "| 房屋内房间总数 | 5 间房间 | 4 间房间 | 8 间房间 |\n",
    "| 社区贫困指数（％被认为是贫困阶层） | 17% | 32% | 3% |\n",
    "| 邻近学校的学生-老师比例 | 15：1 | 22：1 | 12：1 |\n",
    "\n",
    "* 你会建议每位客户的房屋销售的价格为多少？\n",
    "* 从房屋特征的数值判断，这样的价格合理吗？为什么？\n",
    "\n",
    "**提示：**用你在**分析数据**部分计算出来的统计信息来帮助你证明你的答案。\n",
    "\n",
    "运行下列的代码区域，使用你优化的模型来为每位客户的房屋价值做出预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted selling price for Client 1's home: $306,337.50\n",
      "Predicted selling price for Client 2's home: $224,342.55\n",
      "Predicted selling price for Client 3's home: $930,490.91\n"
     ]
    }
   ],
   "source": [
    "# Produce a matrix for client data\n",
    "client_data = [[5, 17, 15], # Client 1\n",
    "               [4, 32, 22], # Client 2\n",
    "               [8, 3, 12]]  # Client 3\n",
    "\n",
    "# Show predictions\n",
    "for i, price in enumerate(reg.predict(client_data)):\n",
    "    print(\"Predicted selling price for Client {}'s home: ${:,.2f}\".format(i+1, price))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 10 - 回答：\n",
    "Predicted selling price for Client 1's home: $306,337.50\n",
    "\n",
    "Predicted selling price for Client 2's home: $224,342.55\n",
    "\n",
    "Predicted selling price for Client 3's home: $930,490.91\n",
    "\n",
    "\n",
    "根据分析数据部分的数据\n",
    "\n",
    "Statistics for Boston housing dataset:\n",
    "\n",
    "Minimum price: $105000.00\n",
    "\n",
    "Maximum price: $1024800.00\n",
    "\n",
    "Mean price: $454342.94\n",
    "\n",
    "数据合理 \n",
    "\n",
    "预测数据最大与最小数据分别为224,342.55和930,490.91，平均值为487057，与原始数据分析的特征较吻合。\n",
    "\n",
    "通常来说房间数越少，价格越低，社区越贫困，代表地区发展水平不好，价格也便宜，社区老师越少，教育水平低，房价也低，综合上述原因，可见预测结果较准确"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 5\n",
    "你刚刚预测了三个客户的房子的售价。在这个练习中，你将用你的最优模型在整个测试数据上进行预测, 并计算相对于目标变量的决定系数 $R^2$ 的值。\n",
    "\n",
    "**提示：**\n",
    "* 你可能需要用到 `X_test`, `y_test`, `reg`, `performance_metric`。\n",
    "* 参考问题10的代码进行预测。\n",
    "* 参考问题2的代码来计算 $R^2$ 的值。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal model has R^2 score 0.71 on test data\n"
     ]
    }
   ],
   "source": [
    "# TODO Calculate the r2 score between 'y_true' and 'y_predict'\n",
    "\n",
    "r2 = performance_metric(y_test,reg.predict(X_test))\n",
    "\n",
    "print(\"Optimal model has R^2 score {:,.2f} on test data\".format(r2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题11 - 分析决定系数\n",
    "\n",
    "你刚刚计算了最优模型在测试集上的决定系数，你会如何评价这个结果？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题11 - 回答\n",
    "\n",
    "决定系数仅为0.71，与问题2的预测相比，模型表现并不太好"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型健壮性\n",
    "\n",
    "一个最优的模型不一定是一个健壮模型。有的时候模型会过于复杂或者过于简单，以致于难以泛化新增添的数据；有的时候模型采用的学习算法并不适用于特定的数据结构；有的时候样本本身可能有太多噪点或样本过少，使得模型无法准确地预测目标变量。这些情况下我们会说模型是欠拟合的。\n",
    "\n",
    "### 问题 12 - 模型健壮性\n",
    "\n",
    "模型是否足够健壮来保证预测的一致性？\n",
    "\n",
    "**提示**: 执行下方区域中的代码，采用不同的训练和测试集执行 `fit_model` 函数10次。注意观察对一个特定的客户来说，预测是如何随训练数据的变化而变化的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trial 1: $391,183.33\n",
      "Trial 2: $411,417.39\n",
      "Trial 3: $415,800.00\n",
      "Trial 4: $420,622.22\n",
      "Trial 5: $413,334.78\n",
      "Trial 6: $411,931.58\n",
      "Trial 7: $390,250.00\n",
      "Trial 8: $407,232.00\n",
      "Trial 9: $402,531.82\n",
      "Trial 10: $413,700.00\n",
      "\n",
      "Range in prices: $30,372.22\n"
     ]
    }
   ],
   "source": [
    "vs.PredictTrials(features, prices, fit_model, client_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 12 - 回答：\n",
    "\n",
    "预测的最大与最小差为$30,372.22，对于预测波动近10%，预测一致性不理想"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 13 - 实用性探讨\n",
    "*简单地讨论一下你建构的模型能否在现实世界中使用？* \n",
    "\n",
    "提示：回答以下几个问题，并给出相应结论的理由：\n",
    "- *1978年所采集的数据，在已考虑通货膨胀的前提下，在今天是否仍然适用？*\n",
    "- *数据中呈现的特征是否足够描述一个房屋？*\n",
    "- *在波士顿这样的大都市采集的数据，能否应用在其它乡镇地区？*\n",
    "- *你觉得仅仅凭房屋所在社区的环境来判断房屋价值合理吗？*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 13 - 回答：\n",
    "\n",
    "不能，经过40年的发展，社区的发展也不相同，房价也可能发生翻天覆地的变化\n",
    "\n",
    "三个特征还不够，还应该从社区安全，交通便利性，医疗水平等方面考虑\n",
    "\n",
    "波士顿采集的数据在其他乡镇地区并不适用，乡镇地区的数据特征显然与大都市不同，房价会更低。\n",
    "\n",
    "房价也要看发展潜力，政府的规划有可能导致某一地区房价保障"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第七步.完成和提交"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当你完成了以上所有的代码和问题，你需要将 iPython Notebook 导出 HTML，导出方法：在左上角的菜单中选择 **File -> Download as -> HTML (.html)**。当你提交项目时，需要包含**可运行的 .ipynb 文件**和**导出的 HTML 文件**。"
   ]
  }
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